Donald Trump has challenged Rex Tillerson to "compare IQ tests" if his secretary of state called the president a "moron", as reported.

Mr Trump told Forbes magazine: "I think it's fake news. But if he did that, I guess we'll have to compare IQ tests. And I can tell you who is going to win."

The president's tense relationship with Mr Tillerson burst into public view last week as an NBC News story claimed vice president Mike Pence had to talk the secretary of state out of resigning this summer, and that Mr Tillerson had called Mr Trump a "moron".

Mr Tillerson said he never considered resigning, and his spokeswoman said he never used such language.

Mr Trump and Mr Tillerson are scheduled to have lunch later with defence secretary Jim Mattis.

Mr Trump has at times appeared to undercut Mr Tillerson's message on some of the US's most sensitive national security challenges, including Iran and North Korea.

Mr Tillerson also has publicly complained about the White House blocking him from making key appointments.

But last week the president told reporters he had "total confidence" in his secretary of state.

In the Forbes interview, Mr Trump responded to criticism that he has undermined his secretary of state through his often provocative tweets that have interfered directly with ongoing diplomatic efforts.

The latest outburst came as he launched another series of tweets on a wide range of topics on Tuesday morning.

He said that reaching out to congressional Democrats for help in getting immigration legislation passed is difficult because "the Democrats don't want secure borders". In his tweet, Mr Trump claimed Democrats "don't care about safety for USA".

His post came two days after he sent an immigration overhaul wish-list of legislative proposals to congressional leaders, including a requirement that Congress agree to a host of border security improvements and make significant changes to the green card programme.

Mr Trump said on Sunday there needed to be security enhancements - and the border wall he has demanded - before he would sign on to a bill restoring a programme that shields from deportation young people brought to the US illegally when they were children.

He also said he would be acting on health care soon: "I will be using the power of the pen to give great HealthCare to many people - FAST."

The White House has been finalising an executive order that would expand health plans offered by associations to allow individuals to pool together and buy insurance outside their states.

The president also suggested the US change its tax laws to punish organisations like the NFL if members are "disrespecting" the national anthem or flag.

The NFL gave up its federal tax-exempt status a couple years ago and now files tax returns as a taxable entity.

He also tweeted that ESPN ratings have "tanked" because of Jemele Hill, the anchor suspended for making political statements on social media.

While NFL viewership is down slightly, ESPN remains among the most popular cable networks, averaging 3 million viewers in prime time.